/*
 * Copyright 1997-2006 Sun Microsystems, Inc.  All Rights Reserved.
 * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
 *
 * This code is free software; you can redistribute it and/or modify it
 * under the terms of the GNU General Public License version 2 only, as
 * published by the Free Software Foundation.  Sun designates this
 * particular file as subject to the "Classpath" exception as provided
 * by Sun in the LICENSE file that accompanied this code.
 *
 * This code is distributed in the hope that it will be useful, but WITHOUT
 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
 * FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
 * version 2 for more details (a copy is included in the LICENSE file that
 * accompanied this code).
 *
 * You should have received a copy of the GNU General Public License version
 * 2 along with this work; if not, write to the Free Software Foundation,
 * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
 *
 * Please contact Sun Microsystems, Inc., 4150 Network Circle, Santa Clara,
 * CA 95054 USA or visit www.sun.com if you need additional information or
 * have any questions.
 */

package org.loon.framework.android.game.core.graphics.geom;

import java.io.Serializable;

/**
 * The <code>QuadCurve2D</code> class defines a quadratic parametric curve
 * segment in {@code (x,y)} coordinate space.
 * <p>
 * This class is only the abstract superclass for all objects that store a 2D
 * quadratic curve segment. The actual storage representation of the coordinates
 * is left to the subclass.
 * 
 * @author Jim Graham
 * @since 1.2
 */
public abstract class QuadCurve2D implements Shape, Cloneable {

	/**
	 * A quadratic parametric curve segment specified with {@code float}
	 * coordinates.
	 * 
	 * @since 1.2
	 */
	public static class Float extends QuadCurve2D implements Serializable {
		/**
		 * The X coordinate of the start point of the quadratic curve segment.
		 * 
		 * @since 1.2
		 * @serial
		 */
		public float x1;

		/**
		 * The Y coordinate of the start point of the quadratic curve segment.
		 * 
		 * @since 1.2
		 * @serial
		 */
		public float y1;

		/**
		 * The X coordinate of the control point of the quadratic curve segment.
		 * 
		 * @since 1.2
		 * @serial
		 */
		public float ctrlx;

		/**
		 * The Y coordinate of the control point of the quadratic curve segment.
		 * 
		 * @since 1.2
		 * @serial
		 */
		public float ctrly;

		/**
		 * The X coordinate of the end point of the quadratic curve segment.
		 * 
		 * @since 1.2
		 * @serial
		 */
		public float x2;

		/**
		 * The Y coordinate of the end point of the quadratic curve segment.
		 * 
		 * @since 1.2
		 * @serial
		 */
		public float y2;

		/**
		 * Constructs and initializes a <code>QuadCurve2D</code> with
		 * coordinates (0, 0, 0, 0, 0, 0).
		 * 
		 * @since 1.2
		 */
		public Float() {
		}

		/**
		 * Constructs and initializes a <code>QuadCurve2D</code> from the
		 * specified {@code float} coordinates.
		 * 
		 * @param x1
		 *            the X coordinate of the start point
		 * @param y1
		 *            the Y coordinate of the start point
		 * @param ctrlx
		 *            the X coordinate of the control point
		 * @param ctrly
		 *            the Y coordinate of the control point
		 * @param x2
		 *            the X coordinate of the end point
		 * @param y2
		 *            the Y coordinate of the end point
		 * @since 1.2
		 */
		public Float(float x1, float y1, float ctrlx, float ctrly, float x2,
				float y2) {
			setCurve(x1, y1, ctrlx, ctrly, x2, y2);
		}

		/**
		 * {@inheritDoc}
		 * 
		 * @since 1.2
		 */
		public double getX1() {
			return (double) x1;
		}

		/**
		 * {@inheritDoc}
		 * 
		 * @since 1.2
		 */
		public double getY1() {
			return (double) y1;
		}

		/**
		 * {@inheritDoc}
		 * 
		 * @since 1.2
		 */
		public Point2D getP1() {
			return new Point2D.Float(x1, y1);
		}

		/**
		 * {@inheritDoc}
		 * 
		 * @since 1.2
		 */
		public double getCtrlX() {
			return (double) ctrlx;
		}

		/**
		 * {@inheritDoc}
		 * 
		 * @since 1.2
		 */
		public double getCtrlY() {
			return (double) ctrly;
		}

		/**
		 * {@inheritDoc}
		 * 
		 * @since 1.2
		 */
		public Point2D getCtrlPt() {
			return new Point2D.Float(ctrlx, ctrly);
		}

		/**
		 * {@inheritDoc}
		 * 
		 * @since 1.2
		 */
		public double getX2() {
			return (double) x2;
		}

		/**
		 * {@inheritDoc}
		 * 
		 * @since 1.2
		 */
		public double getY2() {
			return (double) y2;
		}

		/**
		 * {@inheritDoc}
		 * 
		 * @since 1.2
		 */
		public Point2D getP2() {
			return new Point2D.Float(x2, y2);
		}

		/**
		 * {@inheritDoc}
		 * 
		 * @since 1.2
		 */
		public void setCurve(double x1, double y1, double ctrlx, double ctrly,
				double x2, double y2) {
			this.x1 = (float) x1;
			this.y1 = (float) y1;
			this.ctrlx = (float) ctrlx;
			this.ctrly = (float) ctrly;
			this.x2 = (float) x2;
			this.y2 = (float) y2;
		}

		/**
		 * Sets the location of the end points and control point of this curve
		 * to the specified {@code float} coordinates.
		 * 
		 * @param x1
		 *            the X coordinate of the start point
		 * @param y1
		 *            the Y coordinate of the start point
		 * @param ctrlx
		 *            the X coordinate of the control point
		 * @param ctrly
		 *            the Y coordinate of the control point
		 * @param x2
		 *            the X coordinate of the end point
		 * @param y2
		 *            the Y coordinate of the end point
		 * @since 1.2
		 */
		public void setCurve(float x1, float y1, float ctrlx, float ctrly,
				float x2, float y2) {
			this.x1 = x1;
			this.y1 = y1;
			this.ctrlx = ctrlx;
			this.ctrly = ctrly;
			this.x2 = x2;
			this.y2 = y2;
		}

		/**
		 * {@inheritDoc}
		 * 
		 * @since 1.2
		 */
		public Rectangle2D getBounds2D() {
			float left = Math.min(Math.min(x1, x2), ctrlx);
			float top = Math.min(Math.min(y1, y2), ctrly);
			float right = Math.max(Math.max(x1, x2), ctrlx);
			float bottom = Math.max(Math.max(y1, y2), ctrly);
			return new Rectangle2D.Float(left, top, right - left, bottom - top);
		}

		/*
		 * JDK 1.6 serialVersionUID
		 */
		private static final long serialVersionUID = -8511188402130719609L;
	}

	/**
	 * A quadratic parametric curve segment specified with {@code double}
	 * coordinates.
	 * 
	 * @since 1.2
	 */
	public static class Double extends QuadCurve2D implements Serializable {
		/**
		 * The X coordinate of the start point of the quadratic curve segment.
		 * 
		 * @since 1.2
		 * @serial
		 */
		public double x1;

		/**
		 * The Y coordinate of the start point of the quadratic curve segment.
		 * 
		 * @since 1.2
		 * @serial
		 */
		public double y1;

		/**
		 * The X coordinate of the control point of the quadratic curve segment.
		 * 
		 * @since 1.2
		 * @serial
		 */
		public double ctrlx;

		/**
		 * The Y coordinate of the control point of the quadratic curve segment.
		 * 
		 * @since 1.2
		 * @serial
		 */
		public double ctrly;

		/**
		 * The X coordinate of the end point of the quadratic curve segment.
		 * 
		 * @since 1.2
		 * @serial
		 */
		public double x2;

		/**
		 * The Y coordinate of the end point of the quadratic curve segment.
		 * 
		 * @since 1.2
		 * @serial
		 */
		public double y2;

		/**
		 * Constructs and initializes a <code>QuadCurve2D</code> with
		 * coordinates (0, 0, 0, 0, 0, 0).
		 * 
		 * @since 1.2
		 */
		public Double() {
		}

		/**
		 * Constructs and initializes a <code>QuadCurve2D</code> from the
		 * specified {@code double} coordinates.
		 * 
		 * @param x1
		 *            the X coordinate of the start point
		 * @param y1
		 *            the Y coordinate of the start point
		 * @param ctrlx
		 *            the X coordinate of the control point
		 * @param ctrly
		 *            the Y coordinate of the control point
		 * @param x2
		 *            the X coordinate of the end point
		 * @param y2
		 *            the Y coordinate of the end point
		 * @since 1.2
		 */
		public Double(double x1, double y1, double ctrlx, double ctrly,
				double x2, double y2) {
			setCurve(x1, y1, ctrlx, ctrly, x2, y2);
		}

		/**
		 * {@inheritDoc}
		 * 
		 * @since 1.2
		 */
		public double getX1() {
			return x1;
		}

		/**
		 * {@inheritDoc}
		 * 
		 * @since 1.2
		 */
		public double getY1() {
			return y1;
		}

		/**
		 * {@inheritDoc}
		 * 
		 * @since 1.2
		 */
		public Point2D getP1() {
			return new Point2D.Double(x1, y1);
		}

		/**
		 * {@inheritDoc}
		 * 
		 * @since 1.2
		 */
		public double getCtrlX() {
			return ctrlx;
		}

		/**
		 * {@inheritDoc}
		 * 
		 * @since 1.2
		 */
		public double getCtrlY() {
			return ctrly;
		}

		/**
		 * {@inheritDoc}
		 * 
		 * @since 1.2
		 */
		public Point2D getCtrlPt() {
			return new Point2D.Double(ctrlx, ctrly);
		}

		/**
		 * {@inheritDoc}
		 * 
		 * @since 1.2
		 */
		public double getX2() {
			return x2;
		}

		/**
		 * {@inheritDoc}
		 * 
		 * @since 1.2
		 */
		public double getY2() {
			return y2;
		}

		/**
		 * {@inheritDoc}
		 * 
		 * @since 1.2
		 */
		public Point2D getP2() {
			return new Point2D.Double(x2, y2);
		}

		/**
		 * {@inheritDoc}
		 * 
		 * @since 1.2
		 */
		public void setCurve(double x1, double y1, double ctrlx, double ctrly,
				double x2, double y2) {
			this.x1 = x1;
			this.y1 = y1;
			this.ctrlx = ctrlx;
			this.ctrly = ctrly;
			this.x2 = x2;
			this.y2 = y2;
		}

		/**
		 * {@inheritDoc}
		 * 
		 * @since 1.2
		 */
		public Rectangle2D getBounds2D() {
			double left = Math.min(Math.min(x1, x2), ctrlx);
			double top = Math.min(Math.min(y1, y2), ctrly);
			double right = Math.max(Math.max(x1, x2), ctrlx);
			double bottom = Math.max(Math.max(y1, y2), ctrly);
			return new Rectangle2D.Double(left, top, right - left, bottom - top);
		}

		/*
		 * JDK 1.6 serialVersionUID
		 */
		private static final long serialVersionUID = 4217149928428559721L;
	}

	/**
	 * This is an abstract class that cannot be instantiated directly.
	 * Type-specific implementation subclasses are available for instantiation
	 * and provide a number of formats for storing the information necessary to
	 * satisfy the various accessor methods below.
	 * 
	 * @see and.awt.geom.QuadCurve2D.Float
	 * @see and.awt.geom.QuadCurve2D.Double
	 * @since 1.2
	 */
	protected QuadCurve2D() {
	}

	/**
	 * Returns the X coordinate of the start point in <code>double</code> in
	 * precision.
	 * 
	 * @return the X coordinate of the start point.
	 * @since 1.2
	 */
	public abstract double getX1();

	/**
	 * Returns the Y coordinate of the start point in <code>double</code>
	 * precision.
	 * 
	 * @return the Y coordinate of the start point.
	 * @since 1.2
	 */
	public abstract double getY1();

	/**
	 * Returns the start point.
	 * 
	 * @return a <code>Point2D</code> that is the start point of this
	 *         <code>QuadCurve2D</code>.
	 * @since 1.2
	 */
	public abstract Point2D getP1();

	/**
	 * Returns the X coordinate of the control point in <code>double</code>
	 * precision.
	 * 
	 * @return X coordinate the control point
	 * @since 1.2
	 */
	public abstract double getCtrlX();

	/**
	 * Returns the Y coordinate of the control point in <code>double</code>
	 * precision.
	 * 
	 * @return the Y coordinate of the control point.
	 * @since 1.2
	 */
	public abstract double getCtrlY();

	/**
	 * Returns the control point.
	 * 
	 * @return a <code>Point2D</code> that is the control point of this
	 *         <code>Point2D</code>.
	 * @since 1.2
	 */
	public abstract Point2D getCtrlPt();

	/**
	 * Returns the X coordinate of the end point in <code>double</code>
	 * precision.
	 * 
	 * @return the x coordiante of the end point.
	 * @since 1.2
	 */
	public abstract double getX2();

	/**
	 * Returns the Y coordinate of the end point in <code>double</code>
	 * precision.
	 * 
	 * @return the Y coordinate of the end point.
	 * @since 1.2
	 */
	public abstract double getY2();

	/**
	 * Returns the end point.
	 * 
	 * @return a <code>Point</code> object that is the end point of this
	 *         <code>Point2D</code>.
	 * @since 1.2
	 */
	public abstract Point2D getP2();

	/**
	 * Sets the location of the end points and control point of this curve to
	 * the specified <code>double</code> coordinates.
	 * 
	 * @param x1
	 *            the X coordinate of the start point
	 * @param y1
	 *            the Y coordinate of the start point
	 * @param ctrlx
	 *            the X coordinate of the control point
	 * @param ctrly
	 *            the Y coordinate of the control point
	 * @param x2
	 *            the X coordinate of the end point
	 * @param y2
	 *            the Y coordinate of the end point
	 * @since 1.2
	 */
	public abstract void setCurve(double x1, double y1, double ctrlx,
			double ctrly, double x2, double y2);

	/**
	 * Sets the location of the end points and control points of this
	 * <code>QuadCurve2D</code> to the <code>double</code> coordinates at the
	 * specified offset in the specified array.
	 * 
	 * @param coords
	 *            the array containing coordinate values
	 * @param offset
	 *            the index into the array from which to start getting the
	 *            coordinate values and assigning them to this
	 *            <code>QuadCurve2D</code>
	 * @since 1.2
	 */
	public void setCurve(double[] coords, int offset) {
		setCurve(coords[offset + 0], coords[offset + 1], coords[offset + 2],
				coords[offset + 3], coords[offset + 4], coords[offset + 5]);
	}

	/**
	 * Sets the location of the end points and control point of this
	 * <code>QuadCurve2D</code> to the specified <code>Point2D</code>
	 * coordinates.
	 * 
	 * @param p1
	 *            the start point
	 * @param cp
	 *            the control point
	 * @param p2
	 *            the end point
	 * @since 1.2
	 */
	public void setCurve(Point2D p1, Point2D cp, Point2D p2) {
		setCurve(p1.getX(), p1.getY(), cp.getX(), cp.getY(), p2.getX(), p2
				.getY());
	}

	/**
	 * Sets the location of the end points and control points of this
	 * <code>QuadCurve2D</code> to the coordinates of the <code>Point2D</code>
	 * objects at the specified offset in the specified array.
	 * 
	 * @param pts
	 *            an array containing <code>Point2D</code> that define
	 *            coordinate values
	 * @param offset
	 *            the index into <code>pts</code> from which to start getting
	 *            the coordinate values and assigning them to this
	 *            <code>QuadCurve2D</code>
	 * @since 1.2
	 */
	public void setCurve(Point2D[] pts, int offset) {
		setCurve(pts[offset + 0].getX(), pts[offset + 0].getY(),
				pts[offset + 1].getX(), pts[offset + 1].getY(), pts[offset + 2]
						.getX(), pts[offset + 2].getY());
	}

	/**
	 * Sets the location of the end points and control point of this
	 * <code>QuadCurve2D</code> to the same as those in the specified
	 * <code>QuadCurve2D</code>.
	 * 
	 * @param c
	 *            the specified <code>QuadCurve2D</code>
	 * @since 1.2
	 */
	public void setCurve(QuadCurve2D c) {
		setCurve(c.getX1(), c.getY1(), c.getCtrlX(), c.getCtrlY(), c.getX2(), c
				.getY2());
	}

	/**
	 * Returns the square of the flatness, or maximum distance of a control
	 * point from the line connecting the end points, of the quadratic curve
	 * specified by the indicated control points.
	 * 
	 * @param x1
	 *            the X coordinate of the start point
	 * @param y1
	 *            the Y coordinate of the start point
	 * @param ctrlx
	 *            the X coordinate of the control point
	 * @param ctrly
	 *            the Y coordinate of the control point
	 * @param x2
	 *            the X coordinate of the end point
	 * @param y2
	 *            the Y coordinate of the end point
	 * @return the square of the flatness of the quadratic curve defined by the
	 *         specified coordinates.
	 * @since 1.2
	 */
	public static double getFlatnessSq(double x1, double y1, double ctrlx,
			double ctrly, double x2, double y2) {
		return Line2D.ptSegDistSq(x1, y1, x2, y2, ctrlx, ctrly);
	}

	/**
	 * Returns the flatness, or maximum distance of a control point from the
	 * line connecting the end points, of the quadratic curve specified by the
	 * indicated control points.
	 * 
	 * @param x1
	 *            the X coordinate of the start point
	 * @param y1
	 *            the Y coordinate of the start point
	 * @param ctrlx
	 *            the X coordinate of the control point
	 * @param ctrly
	 *            the Y coordinate of the control point
	 * @param x2
	 *            the X coordinate of the end point
	 * @param y2
	 *            the Y coordinate of the end point
	 * @return the flatness of the quadratic curve defined by the specified
	 *         coordinates.
	 * @since 1.2
	 */
	public static double getFlatness(double x1, double y1, double ctrlx,
			double ctrly, double x2, double y2) {
		return Line2D.ptSegDist(x1, y1, x2, y2, ctrlx, ctrly);
	}

	/**
	 * Returns the square of the flatness, or maximum distance of a control
	 * point from the line connecting the end points, of the quadratic curve
	 * specified by the control points stored in the indicated array at the
	 * indicated index.
	 * 
	 * @param coords
	 *            an array containing coordinate values
	 * @param offset
	 *            the index into <code>coords</code> from which to to start
	 *            getting the values from the array
	 * @return the flatness of the quadratic curve that is defined by the values
	 *         in the specified array at the specified index.
	 * @since 1.2
	 */
	public static double getFlatnessSq(double coords[], int offset) {
		return Line2D.ptSegDistSq(coords[offset + 0], coords[offset + 1],
				coords[offset + 4], coords[offset + 5], coords[offset + 2],
				coords[offset + 3]);
	}

	/**
	 * Returns the flatness, or maximum distance of a control point from the
	 * line connecting the end points, of the quadratic curve specified by the
	 * control points stored in the indicated array at the indicated index.
	 * 
	 * @param coords
	 *            an array containing coordinate values
	 * @param offset
	 *            the index into <code>coords</code> from which to start getting
	 *            the coordinate values
	 * @return the flatness of a quadratic curve defined by the specified array
	 *         at the specified offset.
	 * @since 1.2
	 */
	public static double getFlatness(double coords[], int offset) {
		return Line2D.ptSegDist(coords[offset + 0], coords[offset + 1],
				coords[offset + 4], coords[offset + 5], coords[offset + 2],
				coords[offset + 3]);
	}

	/**
	 * Returns the square of the flatness, or maximum distance of a control
	 * point from the line connecting the end points, of this
	 * <code>QuadCurve2D</code>.
	 * 
	 * @return the square of the flatness of this <code>QuadCurve2D</code>.
	 * @since 1.2
	 */
	public double getFlatnessSq() {
		return Line2D.ptSegDistSq(getX1(), getY1(), getX2(), getY2(),
				getCtrlX(), getCtrlY());
	}

	/**
	 * Returns the flatness, or maximum distance of a control point from the
	 * line connecting the end points, of this <code>QuadCurve2D</code>.
	 * 
	 * @return the flatness of this <code>QuadCurve2D</code>.
	 * @since 1.2
	 */
	public double getFlatness() {
		return Line2D.ptSegDist(getX1(), getY1(), getX2(), getY2(), getCtrlX(),
				getCtrlY());
	}

	/**
	 * Subdivides this <code>QuadCurve2D</code> and stores the resulting two
	 * subdivided curves into the <code>left</code> and <code>right</code> curve
	 * parameters. Either or both of the <code>left</code> and
	 * <code>right</code> objects can be the same as this
	 * <code>QuadCurve2D</code> or <code>null</code>.
	 * 
	 * @param left
	 *            the <code>QuadCurve2D</code> object for storing the left or
	 *            first half of the subdivided curve
	 * @param right
	 *            the <code>QuadCurve2D</code> object for storing the right or
	 *            second half of the subdivided curve
	 * @since 1.2
	 */
	public void subdivide(QuadCurve2D left, QuadCurve2D right) {
		subdivide(this, left, right);
	}

	/**
	 * Subdivides the quadratic curve specified by the <code>src</code>
	 * parameter and stores the resulting two subdivided curves into the
	 * <code>left</code> and <code>right</code> curve parameters. Either or both
	 * of the <code>left</code> and <code>right</code> objects can be the same
	 * as the <code>src</code> object or <code>null</code>.
	 * 
	 * @param src
	 *            the quadratic curve to be subdivided
	 * @param left
	 *            the <code>QuadCurve2D</code> object for storing the left or
	 *            first half of the subdivided curve
	 * @param right
	 *            the <code>QuadCurve2D</code> object for storing the right or
	 *            second half of the subdivided curve
	 * @since 1.2
	 */
	public static void subdivide(QuadCurve2D src, QuadCurve2D left,
			QuadCurve2D right) {
		double x1 = src.getX1();
		double y1 = src.getY1();
		double ctrlx = src.getCtrlX();
		double ctrly = src.getCtrlY();
		double x2 = src.getX2();
		double y2 = src.getY2();
		double ctrlx1 = (x1 + ctrlx) / 2.0;
		double ctrly1 = (y1 + ctrly) / 2.0;
		double ctrlx2 = (x2 + ctrlx) / 2.0;
		double ctrly2 = (y2 + ctrly) / 2.0;
		ctrlx = (ctrlx1 + ctrlx2) / 2.0;
		ctrly = (ctrly1 + ctrly2) / 2.0;
		if (left != null) {
			left.setCurve(x1, y1, ctrlx1, ctrly1, ctrlx, ctrly);
		}
		if (right != null) {
			right.setCurve(ctrlx, ctrly, ctrlx2, ctrly2, x2, y2);
		}
	}

	/**
	 * Subdivides the quadratic curve specified by the coordinates stored in the
	 * <code>src</code> array at indices <code>srcoff</code> through
	 * <code>srcoff</code>&nbsp;+&nbsp;5 and stores the resulting two subdivided
	 * curves into the two result arrays at the corresponding indices. Either or
	 * both of the <code>left</code> and <code>right</code> arrays can be
	 * <code>null</code> or a reference to the same array and offset as the
	 * <code>src</code> array. Note that the last point in the first subdivided
	 * curve is the same as the first point in the second subdivided curve.
	 * Thus, it is possible to pass the same array for <code>left</code> and
	 * <code>right</code> and to use offsets such that <code>rightoff</code>
	 * equals <code>leftoff</code> + 4 in order to avoid allocating extra
	 * storage for this common point.
	 * 
	 * @param src
	 *            the array holding the coordinates for the source curve
	 * @param srcoff
	 *            the offset into the array of the beginning of the the 6 source
	 *            coordinates
	 * @param left
	 *            the array for storing the coordinates for the first half of
	 *            the subdivided curve
	 * @param leftoff
	 *            the offset into the array of the beginning of the the 6 left
	 *            coordinates
	 * @param right
	 *            the array for storing the coordinates for the second half of
	 *            the subdivided curve
	 * @param rightoff
	 *            the offset into the array of the beginning of the the 6 right
	 *            coordinates
	 * @since 1.2
	 */
	public static void subdivide(double src[], int srcoff, double left[],
			int leftoff, double right[], int rightoff) {
		double x1 = src[srcoff + 0];
		double y1 = src[srcoff + 1];
		double ctrlx = src[srcoff + 2];
		double ctrly = src[srcoff + 3];
		double x2 = src[srcoff + 4];
		double y2 = src[srcoff + 5];
		if (left != null) {
			left[leftoff + 0] = x1;
			left[leftoff + 1] = y1;
		}
		if (right != null) {
			right[rightoff + 4] = x2;
			right[rightoff + 5] = y2;
		}
		x1 = (x1 + ctrlx) / 2.0;
		y1 = (y1 + ctrly) / 2.0;
		x2 = (x2 + ctrlx) / 2.0;
		y2 = (y2 + ctrly) / 2.0;
		ctrlx = (x1 + x2) / 2.0;
		ctrly = (y1 + y2) / 2.0;
		if (left != null) {
			left[leftoff + 2] = x1;
			left[leftoff + 3] = y1;
			left[leftoff + 4] = ctrlx;
			left[leftoff + 5] = ctrly;
		}
		if (right != null) {
			right[rightoff + 0] = ctrlx;
			right[rightoff + 1] = ctrly;
			right[rightoff + 2] = x2;
			right[rightoff + 3] = y2;
		}
	}

	/**
	 * Solves the quadratic whose coefficients are in the <code>eqn</code> array
	 * and places the non-complex roots back into the same array, returning the
	 * number of roots. The quadratic solved is represented by the equation:
	 * 
	 * <pre>
	 *     eqn = {C, B, A};
	 *     ax^2 + bx + c = 0
	 * </pre>
	 * 
	 * A return value of <code>-1</code> is used to distinguish a constant
	 * equation, which might be always 0 or never 0, from an equation that has
	 * no zeroes.
	 * 
	 * @param eqn
	 *            the array that contains the quadratic coefficients
	 * @return the number of roots, or <code>-1</code> if the equation is a
	 *         constant
	 * @since 1.2
	 */
	public static int solveQuadratic(double eqn[]) {
		return solveQuadratic(eqn, eqn);
	}

	/**
	 * Solves the quadratic whose coefficients are in the <code>eqn</code> array
	 * and places the non-complex roots into the <code>res</code> array,
	 * returning the number of roots. The quadratic solved is represented by the
	 * equation:
	 * 
	 * <pre>
	 *     eqn = {C, B, A};
	 *     ax^2 + bx + c = 0
	 * </pre>
	 * 
	 * A return value of <code>-1</code> is used to distinguish a constant
	 * equation, which might be always 0 or never 0, from an equation that has
	 * no zeroes.
	 * 
	 * @param eqn
	 *            the specified array of coefficients to use to solve the
	 *            quadratic equation
	 * @param res
	 *            the array that contains the non-complex roots resulting from
	 *            the solution of the quadratic equation
	 * @return the number of roots, or <code>-1</code> if the equation is a
	 *         constant.
	 * @since 1.3
	 */
	public static int solveQuadratic(double eqn[], double res[]) {
		double a = eqn[2];
		double b = eqn[1];
		double c = eqn[0];
		int roots = 0;
		if (a == 0.0) {
			// The quadratic parabola has degenerated to a line.
			if (b == 0.0) {
				// The line has degenerated to a constant.
				return -1;
			}
			res[roots++] = -c / b;
		} else {
			// From Numerical Recipes, 5.6, Quadratic and Cubic Equations
			double d = b * b - 4.0 * a * c;
			if (d < 0.0) {
				// If d < 0.0, then there are no roots
				return 0;
			}
			d = Math.sqrt(d);
			// For accuracy, calculate one root using:
			// (-b +/- d) / 2a
			// and the other using:
			// 2c / (-b +/- d)
			// Choose the sign of the +/- so that b+d gets larger in magnitude
			if (b < 0.0) {
				d = -d;
			}
			double q = (b + d) / -2.0;
			// We already tested a for being 0 above
			res[roots++] = q / a;
			if (q != 0.0) {
				res[roots++] = c / q;
			}
		}
		return roots;
	}

	/**
	 * {@inheritDoc}
	 * 
	 * @since 1.2
	 */
	public boolean contains(double x, double y) {

		double x1 = getX1();
		double y1 = getY1();
		double xc = getCtrlX();
		double yc = getCtrlY();
		double x2 = getX2();
		double y2 = getY2();

		/*
		 * We have a convex shape bounded by quad curve Pc(t) and ine Pl(t).
		 * 
		 * P1 = (x1, y1) - start point of curve P2 = (x2, y2) - end point of
		 * curve Pc = (xc, yc) - control point
		 * 
		 * Pq(t) = P1*(1 - t)^2 + 2*Pc*t*(1 - t) + P2*t^2 = = (P1 - 2*Pc +
		 * P2)*t^2 + 2*(Pc - P1)*t + P1 Pl(t) = P1*(1 - t) + P2*t t = [0:1]
		 * 
		 * P = (x, y) - point of interest
		 * 
		 * Let's look at second derivative of quad curve equation:
		 * 
		 * Pq''(t) = 2 * (P1 - 2 * Pc + P2) = Pq'' It's constant vector.
		 * 
		 * Let's draw a line through P to be parallel to this vector and find
		 * the intersection of the quad curve and the line.
		 * 
		 * Pq(t) is point of intersection if system of equations below has the
		 * solution.
		 * 
		 * L(s) = P + Pq''*s == Pq(t) Pq''*s + (P - Pq(t)) == 0
		 * 
		 * | xq''*s + (x - xq(t)) == 0 | yq''*s + (y - yq(t)) == 0
		 * 
		 * This system has the solution if rank of its matrix equals to 1. That
		 * is, determinant of the matrix should be zero.
		 * 
		 * (y - yq(t))*xq'' == (x - xq(t))*yq''
		 * 
		 * Let's solve this equation with 't' variable. Also let kx = x1 - 2*xc
		 * + x2 ky = y1 - 2*yc + y2
		 * 
		 * t0q = (1/2)*((x - x1)*ky - (y - y1)*kx) / ((xc - x1)*ky - (yc -
		 * y1)*kx)
		 * 
		 * Let's do the same for our line Pl(t):
		 * 
		 * t0l = ((x - x1)*ky - (y - y1)*kx) / ((x2 - x1)*ky - (y2 - y1)*kx)
		 * 
		 * It's easy to check that t0q == t0l. This fact means we can compute t0
		 * only one time.
		 * 
		 * In case t0 < 0 or t0 > 1, we have an intersections outside of shape
		 * bounds. So, P is definitely out of shape.
		 * 
		 * In case t0 is inside [0:1], we should calculate Pq(t0) and Pl(t0). We
		 * have three points for now, and all of them lie on one line. So, we
		 * just need to detect, is our point of interest between points of
		 * intersections or not.
		 * 
		 * If the denominator in the t0q and t0l equations is zero, then the
		 * points must be collinear and so the curve is degenerate and encloses
		 * no area. Thus the result is false.
		 */
		double kx = x1 - 2 * xc + x2;
		double ky = y1 - 2 * yc + y2;
		double dx = x - x1;
		double dy = y - y1;
		double dxl = x2 - x1;
		double dyl = y2 - y1;

		double t0 = (dx * ky - dy * kx) / (dxl * ky - dyl * kx);
		if (t0 < 0 || t0 > 1) {
			return false;
		}

		double xb = kx * t0 * t0 + 2 * (xc - x1) * t0 + x1;
		double yb = ky * t0 * t0 + 2 * (yc - y1) * t0 + y1;
		double xl = dxl * t0 + x1;
		double yl = dyl * t0 + y1;

		return (x >= xb && x < xl) || (x >= xl && x < xb)
				|| (y >= yb && y < yl) || (y >= yl && y < yb);
	}

	/**
	 * {@inheritDoc}
	 * 
	 * @since 1.2
	 */
	public boolean contains(Point2D p) {
		return contains(p.getX(), p.getY());
	}

	/**
	 * Fill an array with the coefficients of the parametric equation in t,
	 * ready for solving against val with solveQuadratic. We currently have: val
	 * = Py(t) = C1*(1-t)^2 + 2*CP*t*(1-t) + C2*t^2 = C1 - 2*C1*t + C1*t^2 +
	 * 2*CP*t - 2*CP*t^2 + C2*t^2 = C1 + (2*CP - 2*C1)*t + (C1 - 2*CP + C2)*t^2
	 * 0 = (C1 - val) + (2*CP - 2*C1)*t + (C1 - 2*CP + C2)*t^2 0 = C + Bt + At^2
	 * C = C1 - val B = 2*CP - 2*C1 A = C1 - 2*CP + C2
	 */
	private static void fillEqn(double eqn[], double val, double c1, double cp,
			double c2) {
		eqn[0] = c1 - val;
		eqn[1] = cp + cp - c1 - c1;
		eqn[2] = c1 - cp - cp + c2;
		return;
	}

	/**
	 * Evaluate the t values in the first num slots of the vals[] array and
	 * place the evaluated values back into the same array. Only evaluate t
	 * values that are within the range <0, 1>, including the 0 and 1 ends of
	 * the range iff the include0 or include1 booleans are true. If an
	 * "inflection" equation is handed in, then any points which represent a
	 * point of inflection for that quadratic equation are also ignored.
	 */
	private static int evalQuadratic(double vals[], int num, boolean include0,
			boolean include1, double inflect[], double c1, double ctrl,
			double c2) {
		int j = 0;
		for (int i = 0; i < num; i++) {
			double t = vals[i];
			if ((include0 ? t >= 0 : t > 0)
					&& (include1 ? t <= 1 : t < 1)
					&& (inflect == null || inflect[1] + 2 * inflect[2] * t != 0)) {
				double u = 1 - t;
				vals[j++] = c1 * u * u + 2 * ctrl * t * u + c2 * t * t;
			}
		}
		return j;
	}

	private static final int BELOW = -2;
	private static final int LOWEDGE = -1;
	private static final int INSIDE = 0;
	private static final int HIGHEDGE = 1;
	private static final int ABOVE = 2;

	/**
	 * Determine where coord lies with respect to the range from low to high. It
	 * is assumed that low <= high. The return value is one of the 5 values
	 * BELOW, LOWEDGE, INSIDE, HIGHEDGE, or ABOVE.
	 */
	private static int getTag(double coord, double low, double high) {
		if (coord <= low) {
			return (coord < low ? BELOW : LOWEDGE);
		}
		if (coord >= high) {
			return (coord > high ? ABOVE : HIGHEDGE);
		}
		return INSIDE;
	}

	/**
	 * Determine if the pttag represents a coordinate that is already in its
	 * test range, or is on the border with either of the two opttags
	 * representing another coordinate that is "towards the inside" of that test
	 * range. In other words, are either of the two "opt" points
	 * "drawing the pt inward"?
	 */
	private static boolean inwards(int pttag, int opt1tag, int opt2tag) {
		switch (pttag) {
		case BELOW:
		case ABOVE:
		default:
			return false;
		case LOWEDGE:
			return (opt1tag >= INSIDE || opt2tag >= INSIDE);
		case INSIDE:
			return true;
		case HIGHEDGE:
			return (opt1tag <= INSIDE || opt2tag <= INSIDE);
		}
	}

	/**
	 * {@inheritDoc}
	 * 
	 * @since 1.2
	 */
	public boolean intersects(double x, double y, double w, double h) {
		// Trivially reject non-existant rectangles
		if (w <= 0 || h <= 0) {
			return false;
		}

		// Trivially accept if either endpoint is inside the rectangle
		// (not on its border since it may end there and not go inside)
		// Record where they lie with respect to the rectangle.
		// -1 => left, 0 => inside, 1 => right
		double x1 = getX1();
		double y1 = getY1();
		int x1tag = getTag(x1, x, x + w);
		int y1tag = getTag(y1, y, y + h);
		if (x1tag == INSIDE && y1tag == INSIDE) {
			return true;
		}
		double x2 = getX2();
		double y2 = getY2();
		int x2tag = getTag(x2, x, x + w);
		int y2tag = getTag(y2, y, y + h);
		if (x2tag == INSIDE && y2tag == INSIDE) {
			return true;
		}
		double ctrlx = getCtrlX();
		double ctrly = getCtrlY();
		int ctrlxtag = getTag(ctrlx, x, x + w);
		int ctrlytag = getTag(ctrly, y, y + h);

		// Trivially reject if all points are entirely to one side of
		// the rectangle.
		if (x1tag < INSIDE && x2tag < INSIDE && ctrlxtag < INSIDE) {
			return false; // All points left
		}
		if (y1tag < INSIDE && y2tag < INSIDE && ctrlytag < INSIDE) {
			return false; // All points above
		}
		if (x1tag > INSIDE && x2tag > INSIDE && ctrlxtag > INSIDE) {
			return false; // All points right
		}
		if (y1tag > INSIDE && y2tag > INSIDE && ctrlytag > INSIDE) {
			return false; // All points below
		}

		// Test for endpoints on the edge where either the segment
		// or the curve is headed "inwards" from them
		// Note: These tests are a superset of the fast endpoint tests
		// above and thus repeat those tests, but take more time
		// and cover more cases
		if (inwards(x1tag, x2tag, ctrlxtag) && inwards(y1tag, y2tag, ctrlytag)) {
			// First endpoint on border with either edge moving inside
			return true;
		}
		if (inwards(x2tag, x1tag, ctrlxtag) && inwards(y2tag, y1tag, ctrlytag)) {
			// Second endpoint on border with either edge moving inside
			return true;
		}

		// Trivially accept if endpoints span directly across the rectangle
		boolean xoverlap = (x1tag * x2tag <= 0);
		boolean yoverlap = (y1tag * y2tag <= 0);
		if (x1tag == INSIDE && x2tag == INSIDE && yoverlap) {
			return true;
		}
		if (y1tag == INSIDE && y2tag == INSIDE && xoverlap) {
			return true;
		}

		// We now know that both endpoints are outside the rectangle
		// but the 3 points are not all on one side of the rectangle.
		// Therefore the curve cannot be contained inside the rectangle,
		// but the rectangle might be contained inside the curve, or
		// the curve might intersect the boundary of the rectangle.

		double[] eqn = new double[3];
		double[] res = new double[3];
		if (!yoverlap) {
			// Both Y coordinates for the closing segment are above or
			// below the rectangle which means that we can only intersect
			// if the curve crosses the top (or bottom) of the rectangle
			// in more than one place and if those crossing locations
			// span the horizontal range of the rectangle.
			fillEqn(eqn, (y1tag < INSIDE ? y : y + h), y1, ctrly, y2);
			return (solveQuadratic(eqn, res) == 2
					&& evalQuadratic(res, 2, true, true, null, x1, ctrlx, x2) == 2 && getTag(
					res[0], x, x + w)
					* getTag(res[1], x, x + w) <= 0);
		}

		// Y ranges overlap. Now we examine the X ranges
		if (!xoverlap) {
			// Both X coordinates for the closing segment are left of
			// or right of the rectangle which means that we can only
			// intersect if the curve crosses the left (or right) edge
			// of the rectangle in more than one place and if those
			// crossing locations span the vertical range of the rectangle.
			fillEqn(eqn, (x1tag < INSIDE ? x : x + w), x1, ctrlx, x2);
			return (solveQuadratic(eqn, res) == 2
					&& evalQuadratic(res, 2, true, true, null, y1, ctrly, y2) == 2 && getTag(
					res[0], y, y + h)
					* getTag(res[1], y, y + h) <= 0);
		}

		// The X and Y ranges of the endpoints overlap the X and Y
		// ranges of the rectangle, now find out how the endpoint
		// line segment intersects the Y range of the rectangle
		double dx = x2 - x1;
		double dy = y2 - y1;
		double k = y2 * x1 - x2 * y1;
		int c1tag, c2tag;
		if (y1tag == INSIDE) {
			c1tag = x1tag;
		} else {
			c1tag = getTag((k + dx * (y1tag < INSIDE ? y : y + h)) / dy, x, x
					+ w);
		}
		if (y2tag == INSIDE) {
			c2tag = x2tag;
		} else {
			c2tag = getTag((k + dx * (y2tag < INSIDE ? y : y + h)) / dy, x, x
					+ w);
		}
		// If the part of the line segment that intersects the Y range
		// of the rectangle crosses it horizontally - trivially accept
		if (c1tag * c2tag <= 0) {
			return true;
		}

		// Now we know that both the X and Y ranges intersect and that
		// the endpoint line segment does not directly cross the rectangle.
		//
		// We can almost treat this case like one of the cases above
		// where both endpoints are to one side, except that we will
		// only get one intersection of the curve with the vertical
		// side of the rectangle. This is because the endpoint segment
		// accounts for the other intersection.
		//
		// (Remember there is overlap in both the X and Y ranges which
		// means that the segment must cross at least one vertical edge
		// of the rectangle - in particular, the "near vertical side" -
		// leaving only one intersection for the curve.)
		//
		// Now we calculate the y tags of the two intersections on the
		// "near vertical side" of the rectangle. We will have one with
		// the endpoint segment, and one with the curve. If those two
		// vertical intersections overlap the Y range of the rectangle,
		// we have an intersection. Otherwise, we don't.

		// c1tag = vertical intersection class of the endpoint segment
		//
		// Choose the y tag of the endpoint that was not on the same
		// side of the rectangle as the subsegment calculated above.
		// Note that we can "steal" the existing Y tag of that endpoint
		// since it will be provably the same as the vertical intersection.
		c1tag = ((c1tag * x1tag <= 0) ? y1tag : y2tag);

		// c2tag = vertical intersection class of the curve
		//
		// We have to calculate this one the straightforward way.
		// Note that the c2tag can still tell us which vertical edge
		// to test against.
		fillEqn(eqn, (c2tag < INSIDE ? x : x + w), x1, ctrlx, x2);
		int num = solveQuadratic(eqn, res);

		// Note: We should be able to assert(num == 2); since the
		// X range "crosses" (not touches) the vertical boundary,
		// but we pass num to evalQuadratic for completeness.
		evalQuadratic(res, num, true, true, null, y1, ctrly, y2);

		// Note: We can assert(num evals == 1); since one of the
		// 2 crossings will be out of the [0,1] range.
		c2tag = getTag(res[0], y, y + h);

		// Finally, we have an intersection if the two crossings
		// overlap the Y range of the rectangle.
		return (c1tag * c2tag <= 0);
	}

	/**
	 * {@inheritDoc}
	 * 
	 * @since 1.2
	 */
	public boolean intersects(Rectangle2D r) {
		return intersects(r.getX(), r.getY(), r.getWidth(), r.getHeight());
	}

	/**
	 * {@inheritDoc}
	 * 
	 * @since 1.2
	 */
	public boolean contains(double x, double y, double w, double h) {
		if (w <= 0 || h <= 0) {
			return false;
		}
		// Assertion: Quadratic curves closed by connecting their
		// endpoints are always convex.
		return (contains(x, y) && contains(x + w, y) && contains(x + w, y + h) && contains(
				x, y + h));
	}

	/**
	 * {@inheritDoc}
	 * 
	 * @since 1.2
	 */
	public boolean contains(Rectangle2D r) {
		return contains(r.getX(), r.getY(), r.getWidth(), r.getHeight());
	}

	/**
	 * {@inheritDoc}
	 * 
	 * @since 1.2
	 */
	public Rectangle getBounds() {
		return getBounds2D().getBounds();
	}

	/**
	 * Returns an iteration object that defines the boundary of the shape of
	 * this <code>QuadCurve2D</code>. The iterator for this class is not
	 * multi-threaded safe, which means that this <code>QuadCurve2D</code> class
	 * does not guarantee that modifications to the geometry of this
	 * <code>QuadCurve2D</code> object do not affect any iterations of that
	 * geometry that are already in process.
	 * 
	 * @param at
	 *            an optional {@link AffineTransform} to apply to the shape
	 *            boundary
	 * @return a {@link PathIterator} object that defines the boundary of the
	 *         shape.
	 * @since 1.2
	 */
	public PathIterator getPathIterator(AffineTransform at) {
		return new QuadIterator(this, at);
	}

	/**
	 * Returns an iteration object that defines the boundary of the flattened
	 * shape of this <code>QuadCurve2D</code>. The iterator for this class is
	 * not multi-threaded safe, which means that this <code>QuadCurve2D</code>
	 * class does not guarantee that modifications to the geometry of this
	 * <code>QuadCurve2D</code> object do not affect any iterations of that
	 * geometry that are already in process.
	 * 
	 * @param at
	 *            an optional <code>AffineTransform</code> to apply to the
	 *            boundary of the shape
	 * @param flatness
	 *            the maximum distance that the control points for a subdivided
	 *            curve can be with respect to a line connecting the end points
	 *            of this curve before this curve is replaced by a straight line
	 *            connecting the end points.
	 * @return a <code>PathIterator</code> object that defines the flattened
	 *         boundary of the shape.
	 * @since 1.2
	 */
	public PathIterator getPathIterator(AffineTransform at, double flatness) {
		return new FlatteningPathIterator(getPathIterator(at), flatness);
	}

	/**
	 * Creates a new object of the same class and with the same contents as this
	 * object.
	 * 
	 * @return a clone of this instance.
	 * @exception OutOfMemoryError
	 *                if there is not enough memory.
	 * @see java.lang.Cloneable
	 * @since 1.2
	 */
	public Object clone() {
		try {
			return super.clone();
		} catch (CloneNotSupportedException e) {
			// this shouldn't happen, since we are Cloneable
			throw new InternalError();
		}
	}
}
